Ball milling, which is especially useful in milling clinker for the production of cement, uses a rotary vessel into which the clinker is introduced and which contains a multiplicity of grinding elements which tumble with the clinker and thereby comminute it. The powdered product is separated from the grinding elements by, for example, screening. The grindihg elements hitherto used for this purpose are balls of a steel alloy with a high content of over 0.45 weight percent carbon. These steel alloys and especially their carbon content are so selected that the resulting grinding balls can be subjected to a hardening process and exhibit, as a result, considerable hardness. The diameters of the balls are chosen for the particular milling result desired. On one hand they must produce a milled product having optimum quality and on the other hand they must undergo a minimum of attrition so that the attrition dose not contaminate the resulting milled product The purity of the product should be if possible quantitative. The grinding balls heretofore in use inevitably undergo certain amount of attrition and must be replaced frequently.